Mixing and Decoherence to Nearest Separable States

TL;DR

This paper investigates how entangled quantum states involving a system and an apparatus evolve towards separable states through decoherence, highlighting the transition from quantum to classical correlations in measurement processes.

Contribution

It introduces a framework for measuring entanglement in pure-mixed states and demonstrates numerically that decoherence drives these states toward the nearest separable state, with increased mixing.

Findings

Entangled states tend toward the nearest separable state during decoherence.

Decoherence causes the quantum correlation to diminish, leaving classical correlation.

States exhibit a tendency toward equal mixing among apparatus states.

Abstract

We consider a class of entangled states of a quantum system (S) and a second system (A) where pure states of the former are correlated with mixed states of the latter, and work out the entanglement measure with reference to the nearest separable state. Such `pure-mixed' entanglement is expected when the system S interacts with a macroscopic measuring apparatus in a quantum measurement, where the quantum correlation is destroyed in the process of environment-induced decoherence whereafter only the classical correlation between S and A remains, the latter being large compared to the former. We present numerical evidence that the entangled S-A state drifts towards the nearest separable state through decoherence, with an additional tendency of equimixing among relevant groups of apparatus states.